A valve drive of this general type is known from the class-forming WO 89/02975. On one hand, it should be stressed that this valve drive is relatively complicated to produce. The master and slave pistons have a common housing. Consequently, this valve drive is built, if necessary, relatively tall or its variability in use is limited. On the other hand, it should also be stressed that the hydraulic backlash compensation element is in permanent hydraulic medium contact with a feed line from the cylinder head. Due to this constant feeding with hydraulic medium, in the most unfavorable case, the backlash compensation element can be unnecessarily “pumped up” outside of the cam base-circle phases and thus undesired stroke changes on the gas-exchange valve can occur.